Unfortunately there have been no definitive studies performed to answer this question. I am part of a team that is developing patient reported outcomes measures to help measure patient satisfaction after facial aesthetic treatments. Hopefully we will have real data to answer this question for you in a few years. That being said to address your problem fat removal versus redistribution is only one piece of the solution. There are several things that must be addressed here to ensure an excellent result.What is this caused by?:There is a ligament that tethers the skin at the junction of your cheek and eyelid (arcus marginalis). There is fat that pushes out from within your globe that is held back by a structure called the orbital septum. There is fat in the cheek and face that descends as a normal aspect of aging. There are medical conditions that make swelling worse, or the contents of the globe push out more. These should be addressed if present and will be discussed with your plastic surgeon.Treatment:There are multiple approaches to treat this condition surgically.The structures can be approached either directly through the skin crease or within the eyelid.The ligament must be released.The fat prolapsing needs to be adjusted, sculpted, blended and in some cases removed to ensure the best cheek contour possible.Finally your lower eyelid must be supported, and muscles tightened to ensure your eyelid heals well and in the correct position. Over the years I have moved more and more into fat preservation and redistribution. Fat is precious in the face after all. However I also customize it to the patient. If you have prominent bone structure in comparison to your eye (deeper set eyes), I never remove fat. If your cheek is very recessed in comparison to your globe, and the fat doesn't blend adequately into your cheek, I will remove some fat conservatively at the time of surgery- think of it as sculpting what is there for shape more than removing. There are many ways to treat your concern and even though I am a craniofacial expert, I cannot say that my approach is right and the other approaches are wrong. Not until the science catches up to the art can I say this to you with a clean conscience. Therefore choose the surgeon that you trust and have a good relationship with. Ideally someone with experience and that also keeps up with the science. Both the surgeons you have seen may get you the result that you are looking for. Please make sure they are a board certified plastic surgeon!